Let \(\lambda _{f}(n)\) be the n-th normalized Fourier coefficient of primitive holomorphic cusp form of even integral weight \(k\ge 2\) for the full modular group \(SL(2,\mathbb {Z})\). In this paper, we first refine related previous results on the l-th power sums of the Fourier coefficient \(\lambda _f(n)\). Then we establish asymptotic formulas of the variance of \(\lambda _f^l(n)\).

中文翻译：

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关于尖点型傅立叶系数的渐近分布

设\(\lambda _{f } (n)\)为全模群\ (SL(2 , \mathbb {Z})\)。在本文中，我们首先对傅立叶系数\(\lambda _f(n)\)的l次方和的相关先前结果进行了改进。然后我们建立\(\lambda _f^l(n)\)方差的渐近公式。